Interface crack between magnetoelectroelastic and orthotropic half-spaces under in-plane loading

Abstract

In this paper, an interface crack between magnetoelectroelastic and orthotropic half-spaces has been studied in detail. By using integral transform techniques the present mixed boundary value problem was reduced to the solution of singular integral equations, which can be further reduced to solving a Riemann-Hilbert problem with closed form solution. The crack-tip singularities of the interface crack have been investigated for possible combinations of the magnetoelectroelastic and orthotropic materials, a criterion based on the coefficient of the Riemann-Hilbert problem is introduced to study the possible singularity behavior of the interface crack, and it is shown that there can be either oscillatory or non-oscillatory singularity for the interface crack depending on the particular combination of the bi-materials. A closed form solution for stresses, electric fields, magnetic fields, electric displacement and magnetic induction in the cracked biomaterials is given, and of particular interests, the analytical expression of the stresses, electric displacements and magnetic inductions along the interface has been obtained.